On the product of the extreme zeros of Laguerre polynomials
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929500196962304 |
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| author | Castillo, K. |
| author_facet | Castillo, K. |
| contents | The purpose of this note is twofold: firstly, it intends to bring to light an apparently unknown property of the product of the extreme zeros of Laguerre polynomials, which in a very particular case leads to a twenty-year-old conjecture for Hermite polynomials posed by Gazeau, Josse-Michaux, and Moncea while developing numerical methods in quantum mechanics; and secondly to progress towards the solution of this problem as an application of a parametric eigenvalue problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the product of the extreme zeros of Laguerre polynomials Castillo, K. Classical Analysis and ODEs 15A18, 47B36 The purpose of this note is twofold: firstly, it intends to bring to light an apparently unknown property of the product of the extreme zeros of Laguerre polynomials, which in a very particular case leads to a twenty-year-old conjecture for Hermite polynomials posed by Gazeau, Josse-Michaux, and Moncea while developing numerical methods in quantum mechanics; and secondly to progress towards the solution of this problem as an application of a parametric eigenvalue problem. |
| title | On the product of the extreme zeros of Laguerre polynomials |
| topic | Classical Analysis and ODEs 15A18, 47B36 |
| url | https://arxiv.org/abs/2409.09405 |